Re: Eiffel Tower: Formula, Patrick Weidman?

[gruhn]

on metal fatigue. =A0a normal dynamic building has a design life of 30 yea= rs

> due to metal fatigue. =A0how come the eiffel tower can stand up so long?

Is the Eiffel Tower a "normal dynamic building"?

[gruhn]

The account at physorg.com is woefully inadequate at describing the problem. It does contain this gem though

Which suggest that it is a lenticular truss.

Which is what Zalewski and Allen suggest in

The physorg article also states that "The tower is composed of four arched, wrought-iron legs tapering inward to form a single column that rises to 300 meters, or 986 feet." but kind of skips over the fact that the arches are not part of the structure. I'd even pick a nit with them that the legs do not taper. The tower tapers, the legs are, each (that's the critical bit) of (apparent) constant cross section to the first deck. Second and this sections do appear to taper the corner "members".

I think what the "problem" is saying is that the apparent curve of the tower does not conform to any relatively plain function we can dream up; but some guy did some numerical analysis and popped out a "single equation" which is messy but does the job (questions arrise here as to what he used for data points and what he discarded as not relevant) but that single equation is in DiffEq land so it has many different equations as solutions, please find one; so yer man in Colorado said "dig, he fudged the bottom so we need two equations."

In the end, the article hints at the pointlessness of all this. It appears that what Eiffel et al really did was draw the tower pretty and according to lenticular properties and then, using the drawing solve the tower graphically (see Zalewski and Allen again).

The orignal question "what equation did Eiffel use" seems to just be wrong and a side effect of number crunching modern engineers. See

Make it look pretty then let the engineers keep it upright.

[gruhn]

Seems to me that the question isn't regarding solving the individual members, or even the larger ones, but rather describing the shape.